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        <h2>
          <span class="refentrytitle">filter2</span>
        </h2>
        <p>filter2 — 
      Performs filtering using a transposed form-II digital filter lattice with no time-varying control.
    </p>
      </div>
      <div class="refsect1">
        <a id="idp103067744"></a>
        <h2>Description</h2>
        <p>
      General purpose custom filter with no time-varying pole control. The filter coefficients implement the following difference equation:
      </p>
        <div class="literallayout">
          <p><br />
(1)*y(n) = b0*x[n] + b1*x[n-1] +...+ bM*x[n-M] - a1*y[n-1] -...- aN*y[n-N]<br />
      </p>
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        <p>
    </p>
        <p>
      the system function for which is represented by:
      </p>
        <div class="literallayout">
          <p><br />
           B(Z)      b0 + b1*Z<sup>-1</sup>  + ... + bM*Z<sup>-M</sup><br />
  H(Z)  =  ----  =  --------------------------<br />
           A(Z)       1 + a1*Z<sup>-1</sup>  + ... + aN*Z<sup>-N</sup><br />
      </p>
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        <p>
    </p>
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      <div class="refsect1">
        <a id="idp103132752"></a>
        <h2>Syntax</h2>
        <pre class="synopsis">ares <span class="command"><strong>filter2</strong></span> asig, iM, iN, ib0, ib1, ..., ibM, ia1, ia2, ..., iaN</pre>
        <pre class="synopsis">kres <span class="command"><strong>filter2</strong></span> ksig, iM, iN, ib0, ib1, ..., ibM, ia1, ia2, ..., iaN</pre>
      </div>
      <div class="refsect1">
        <a id="idp103136432"></a>
        <h2>Initialization</h2>
        <p>
      At initialization the number of zeros and poles of the filter are specified along with the corresponding zero and pole coefficients. The coefficients must be obtained by an external filter-design application such as Matlab and specified directly or loaded into a table via <a class="link" href="GEN01.html" title="GEN01"><em class="citetitle">GEN01</em></a>.
    </p>
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      <div class="refsect1">
        <a id="idp103138880"></a>
        <h2>Performance</h2>
        <p>
      The<span class="emphasis"><em> filter2</em></span> opcodes perform filtering using a transposed form-II digital filter lattice with no time-varying control.
    </p>
        <p>
      Since <span class="emphasis"><em>filter2</em></span> implements generalized recursive filters, it can be used to specify a large range of general DSP algorithms. For example, a digital waveguide can be implemented for musical instrument modeling using a pair of <a class="link" href="delayr.html" title="delayr"><em class="citetitle">delayr</em></a> and <a class="link" href="delayw.html" title="delayw"><em class="citetitle">delayw</em></a> opcodes in conjunction with the <span class="emphasis"><em>filter2</em></span> opcode.
    </p>
      </div>
      <div class="refsect1">
        <a id="idp103144080"></a>
        <h2>Examples</h2>
        <p>
      A first-order linear-phase lowpass FIR filter operating on a k-rate signal:

      </p>
        <div class="informalexample">
          <pre class="programlisting">
k1 <span class="opc">filter2</span> ksig, 2, 0, 0.5, 0.5   <span class="comment">;; k-rate FIR filter</span></pre>
        </div>
        <p>
    </p>
        <p>
      Here is another example of the filter2 opcode. It uses the file <a class="ulink" href="examples/filter2.csd" target="_top"><em class="citetitle">filter2.csd</em></a>.
            </p>
        <div class="example">
          <a id="idp103148768"></a>
          <p class="title">
            <strong>Example 257. Example of the filter2 opcode.</strong>
          </p>
          <div class="example-contents">
            <p>See the sections <a class="link" href="UsingRealTime.html" title="Real-Time Audio"><em class="citetitle">Real-time Audio</em></a> and <a class="link" href="CommandFlags.html" title="Csound command line"><em class="citetitle">Command Line Flags</em></a> for more information on using command line flags.</p>
            <pre class="programlisting">
<span class="csdtag">&lt;CsoundSynthesizer&gt;</span>
<span class="csdtag">&lt;CsOptions&gt;</span>
<span class="comment">; Select audio/midi flags here according to platform</span>
-odac   <span class="comment">;;;realtime audio out</span>
<span class="comment">;-iadc    ;;;uncomment -iadc if realtime audio input is needed too</span>
<span class="comment">; For Non-realtime ouput leave only the line below:</span>
<span class="comment">; -o filter2.wav -W ;;; for file output any platform</span>
<span class="csdtag">&lt;/CsOptions&gt;</span>
<span class="csdtag">&lt;CsInstruments&gt;</span>

<span class="ohdr">sr</span> <span class="op">=</span> 44100
<span class="ohdr">ksmps</span> <span class="op">=</span> 32
<span class="ohdr">nchnls</span> <span class="op">=</span> 2
<span class="ohdr">0dbfs</span>  <span class="op">=</span> 1

<span class="oblock">instr</span> 1	 <span class="comment">; 2 saw waves of which one is slightly detuned</span>
 
ib1   <span class="op">=</span> p5  
ivol  <span class="op">=</span> p6				<span class="comment">;volume to compensate                                               </span>
kcps  <span class="opc">init</span> <span class="opc">cpspch</span>(p4)
asig1 <span class="opc">vco2</span> .05, kcps			<span class="comment">;saw 1</span>
asaw1 <span class="opc">filter2</span> asig1, 1, 1, 1, ib1	<span class="comment">;filter 1 </span>
asig2 <span class="opc">vco2</span> .05, kcps<span class="op">+</span>1			<span class="comment">;saw 2                      </span>
asaw2 <span class="opc">filter2</span> asig2, 1, 1, 1, ib1	<span class="comment">;filter 2</span>
aout  <span class="op">=</span> (asaw1<span class="op">+</span>asaw2)<span class="op">*</span>ivol		<span class="comment">;mix</span>
      <span class="opc">outs</span> aout, aout

<span class="oblock">endin</span>
<span class="csdtag">&lt;/CsInstruments&gt;</span>
<span class="csdtag">&lt;CsScore&gt;</span>

<span class="stamnt">i</span> 1 0 4 6.00 -.001 5	<span class="comment">;different filter values</span>
<span class="stamnt">i</span> 1 + 4 6.00 -.6   2	<span class="comment">;and different volumes</span>
<span class="stamnt">i</span> 1 + 4 6.00 -.95 .3	<span class="comment">;to compensate</span>
<span class="stamnt">e</span>
<span class="csdtag">&lt;/CsScore&gt;</span>
<span class="csdtag">&lt;/CsoundSynthesizer&gt;</span>
</pre>
          </div>
        </div>
        <p><br class="example-break" />
    </p>
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      <div class="refsect1">
        <a id="idp103153056"></a>
        <h2>See Also</h2>
        <p>
      <a class="link" href="zfilter2.html" title="zfilter2"><em class="citetitle">zfilter2</em></a>
    </p>
      </div>
      <div class="refsect1">
        <a id="idp103155104"></a>
        <h2>Credits</h2>
        <p>
      </p>
        <table border="0" summary="Simple list" class="simplelist">
          <tr>
            <td>Author: Michael A. Casey</td>
          </tr>
          <tr>
            <td>M.I.T.</td>
          </tr>
          <tr>
            <td>Cambridge, Mass.</td>
          </tr>
          <tr>
            <td>1997</td>
          </tr>
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        <p>
    </p>
        <p>New in version 3.47</p>
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